cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 13 results. Next

A215731 a(n) is the smallest m for which the decimal representation of 11^m contains n consecutive identical digits.

Original entry on oeis.org

0, 1, 8, 39, 156, 482, 1323, 2983, 9443, 39879, 214747, 296095, 296095, 5541239, 8621384, 30789328
Offset: 1

Views

Author

V. Raman, Aug 22 2012

Keywords

Examples

			The decimal representation of 11^39879 contains ten consecutive 6s, and is the least such power with such a string of digits.

Crossrefs

Cf. A215737 (the repeated digits), A045875, A215727, A215728, A215729, A215730.

Programs

  • Mathematica
    mostDigits[t_] := Module[{lastDigit = t[[1]], record = 1, cnt = 1}, Do[If[t[[n]] == lastDigit, cnt++, If[cnt > record, record = cnt]; cnt = 1; lastDigit = t[[n]]], {n, 2, Length[t]}]; If[cnt > record, record = cnt] ; record]; nn = 10; t = Table[-1, {nn}]; n = -1; While[Min[t] == -1, n++; c = mostDigits[IntegerDigits[11^n]]; If[c > nn, c = nn]; While[c > 0 && t[[c]] == -1, t[[c]] = n; c--]]; t (* T. D. Noe, Apr 29 2013 *)
  • Python
    def A215731(n):
    l, x = [str(d)*n for d in range(10)], 1
    for m in range(10**9):
        s = str(x)
        for k in l:
            if k in s:
                return m
        x *= 11
    return 'search limit reached'
# Chai Wah Wu, Dec 17 2014

Extensions

a(10) discovered by "Wick" (See http://www.mersenneforum.org/showpost.php?p=334789&postcount=89). Definition clarified and all terms to a(10) verified by Daran Gill, Mar 24 2013
a(11) discovered by Tom Womack (See http://www.mersenneforum.org/showpost.php?p=337916&postcount=105), Rick van der Hoorn, Apr 24 2013
a(12)-a(13) from Giovanni Resta, Apr 25 2013
Corrected a(12), Rick van der Hoorn, Apr 28 2013
a(14) from Giovanni Resta, Apr 18 2016
a(15) from Bert Dobbelaere, Feb 15 2019
a(16) from Paul Geneau de Lamarlière, Oct 03 2024

A215735 a(n) is the first digit to appear n times in succession in a power of 6.

Original entry on oeis.org

1, 7, 7, 0, 2, 1, 2, 7, 1, 1, 0, 5, 7, 6, 3, 7
Offset: 1

Views

Author

V. Raman, Aug 22 2012

Keywords

Crossrefs

See A215729 for the powers.
Cf. A045875, A215732.

Extensions

a(11) added by V. Raman, Nov 23 2013
a(12)-a(13) from Giovanni Resta, Apr 19 2016
a(14) from Bert Dobbelaere, Feb 15 2019
a(15) from Paul Geneau de Lamarlière, Jun 26 2024
a(16) from Paul Geneau de Lamarlière, Jul 12 2024

A217157 a(n) is the least value of k such that the decimal expansion of n^k contains two consecutive identical digits.

Original entry on oeis.org

16, 11, 8, 11, 5, 6, 6, 6, 2, 1, 2, 9, 3, 2, 4, 7, 5, 5, 2, 2, 1, 6, 4, 6, 5, 4, 8, 5, 2, 6, 5, 1, 2, 2, 3, 7, 2, 4, 2, 5, 3, 4, 1, 3, 2, 2, 3, 3, 2, 7, 4, 3, 6, 1, 4, 4, 2, 4, 2, 3, 2, 3, 3, 2, 1, 2, 3, 4, 2, 3, 7, 6, 3, 6, 2, 1, 3, 4, 2, 3, 3, 2, 5, 2, 4, 6
Offset: 2

Views

Author

V. Raman, Sep 27 2012

Keywords

Comments

Least number m such that n^m is a term of A171901 - Chai Wah Wu, Feb 20 2019
Conjecture: 1 <= a(n) <= 16 for n > 1 and a(n) < 16 for n > 2. - Chai Wah Wu, Feb 20 2019
a(n) >= 1 for all n > 1 and is bounded: see link for proof. - Robert Israel, Feb 21 2019

Links

Crossrefs

Cf. A045875, A215236.
Cf. A215727, A215728, A215729, A215730, A215731, A171901, A306305.

Programs

  • Maple
    f:= proc(n) local L,k;
   for k from 1 do
      L:= convert(n^k,base,10);
      if has(L[2..-1]-L[1..-2],0) then return k fi
   od
end proc:
map(f, [$2..100]); # Robert Israel, Feb 21 2019
  • Mathematica
    Table[k = 1; While[! MemberQ[Differences[IntegerDigits[n^k]], 0], k++]; k, {n, 2, 100}] (* T. D. Noe, Oct 01 2012 *)
  • Python
    def A217157(n):
    m, k = 1, n
    while True:
        s = str(k)
        for i in range(1,len(s)):
            if s[i] == s[i-1]:
                return m
        m += 1
        k *= n # Chai Wah Wu, Feb 20 2019

Formula

a(A171901(n)) = 1. - Chai Wah Wu, Feb 20 2019
a(n) = A215236(n) + 1. - Georg Fischer, Nov 25 2020

A217158 a(n) is the least value of k such that the decimal expansion of n^k contains three consecutive identical digits.

Original entry on oeis.org

24, 32, 12, 50, 5, 31, 8, 16, 3, 8, 17, 25, 14, 23, 6, 12, 6, 9, 3, 11, 7, 15, 14, 25, 11, 11, 10, 5, 3, 7, 8, 10, 10, 18, 9, 15, 2, 12, 3, 14, 4, 7, 12, 18, 12, 8, 17, 17, 3, 15, 10, 7, 11, 25, 24, 8, 11, 10, 3, 14, 11, 18, 4, 7, 9, 13, 7, 12, 3, 11, 8, 13
Offset: 2

Views

Author

V. Raman, Sep 27 2012

Keywords

Links

Crossrefs

Cf. A045875, A215727, A215728, A215729, A215730, A215731.

Programs

  • Mathematica
    Table[k = 1; While[! MemberQ[Partition[Differences[IntegerDigits[n^k]], 2, 1], {0, 0}], k++]; k, {n, 2, 100}] (* T. D. Noe, Oct 01 2012 *)
lvk[n_]:=Module[{k=1},While[SequenceCount[IntegerDigits[n^k],{x_,x_,x_}]<1,k++];k]; Array[lvk,80,2] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 13 2018 *)

A217159 a(n) is the least value of k such that the decimal expansion of n^k contains four consecutive identical digits.

Original entry on oeis.org

41, 33, 90, 95, 115, 71, 60, 88, 4, 39, 18, 25, 14, 98, 45, 52, 78, 70, 4, 29, 42, 35, 41, 48, 44, 11, 21, 37, 4, 18, 36, 71, 34, 18, 64, 20, 39, 32, 4, 40, 20, 20, 45, 33, 33, 14, 36, 40, 4, 37, 42, 29, 39, 63, 24, 10, 26, 10, 4, 64, 15, 30, 30, 18, 17, 58
Offset: 2

Views

Author

V. Raman, Sep 27 2012

Keywords

Comments

The term 76 appears for the first time in this sequence at n = 112044721958. - Paul Geneau de Lamarlière, Jun 25 2024

Links

Crossrefs

Cf. A045875, A215727, A215728, A215729, A215730, A215731.

Programs

  • Mathematica
    Table[k = 1; While[! MemberQ[Partition[Differences[IntegerDigits[n^k]], 3, 1], {0, 0, 0}], k++]; k, {n, 2, 100}] (* T. D. Noe, Oct 01 2012 *)
lk[n_]:=Module[{k=1,t=Table[x_,4]},While[SequenceCount[IntegerDigits[n^k],t]< 1,k++];k];Array[lk,80,2] (* Harvey P. Dale, Jun 21 2022 *)

A217160 a(n) is the least value of k such that the decimal expansion of n^k contains five consecutive identical digits.

Original entry on oeis.org

220, 274, 110, 125, 226, 172, 105, 137, 5, 156, 40, 227, 196, 216, 55, 235, 78, 115, 5, 104, 133, 187, 126, 93, 115, 110, 21, 163, 5, 40, 44, 159, 104, 110, 113, 20, 200, 205, 5, 119, 142, 116, 90, 145, 156, 136, 37, 86, 5, 37, 62, 119, 85, 91, 107, 142, 40
Offset: 2

Views

Author

V. Raman, Sep 27 2012

Keywords

Links

Crossrefs

Cf. A045875, A215727, A215728, A215729, A215730, A215731.

Programs

  • Mathematica
    Table[k = 1; While[! MemberQ[Partition[Differences[IntegerDigits[n^k]], 4, 1], {0, 0, 0, 0}], k++]; k, {n, 2, 100}] (* T. D. Noe, Oct 01 2012 *)

A217161 a(n) is the least value of k such that the decimal expansion of n^k contains six consecutive identical digits.

Original entry on oeis.org

971, 538, 486, 1087, 371, 175, 324, 269, 6, 482, 362, 327, 196, 516, 243, 350, 288, 144, 6, 895, 822, 238, 481, 1137, 281, 180, 127, 358, 6, 286, 454, 286, 347, 110, 481, 346, 314, 448, 6, 565, 388, 275, 90, 622, 231, 451, 37, 255, 6, 481, 202, 191, 472, 308
Offset: 2

Views

Author

V. Raman, Sep 27 2012

Keywords

Links

Crossrefs

Cf. A045875, A215727, A215728, A215729, A215730, A215731.

Programs

  • Mathematica
    Table[k = 1; While[! MemberQ[Partition[Differences[IntegerDigits[n^k]], 5, 1], {0, 0, 0, 0, 0}], k++]; k, {n, 2, 100}] (* T. D. Noe, Oct 01 2012 *)
lk[n_]:=Module[{k=1,t=Table[x_,6]},While[SequenceCount[IntegerDigits[ n^k],t]<1,k++];k]; Array[lk,60,2] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 18 2018 *)

A217162 a(n) is the least value of k such that the decimal expansion of n^k contains seven consecutive identical digits.

Original entry on oeis.org

972, 2124, 486, 2786, 1503, 1961, 324, 1062, 7, 1323, 1938, 512, 1053, 2600, 243, 2474, 1486, 940, 7, 1085, 1068, 238, 2908, 1393, 699, 708, 704, 1566, 7, 286, 1711, 935, 2225, 1190, 1357, 692, 1182, 448, 7, 885, 1349, 815, 647, 1675, 1131, 548, 333, 1154, 7
Offset: 2

Views

Author

V. Raman, Sep 27 2012

Keywords

Links

Crossrefs

Cf. A045875, A215727, A215728, A215729, A215730, A215731.

Programs

  • Mathematica
    Table[k = 1; While[! MemberQ[Partition[Differences[IntegerDigits[n^k]], 6, 1], {0, 0, 0, 0, 0, 0}], k++]; k, {n, 2, 100}] (* T. D. Noe, Oct 01 2012 *)
scd[n_]:=Module[{k=1},While[FreeQ[IntegerDigits[n^k],{_,x_,x_,x_,x_,x_,x_,x_,_}],k++];k]; Array[scd,50,2] (* Harvey P. Dale, May 23 2016 *)

A217163 a(n) is the least value of k such that the decimal expansion of n^k contains eight or more consecutive identical digits.

Original entry on oeis.org

8554, 7720, 4277, 2790, 8533, 6176, 4442, 3860, 8, 2983, 2430, 5482, 1053, 5030, 3502, 5781, 3982, 4706, 8, 2568, 4850, 2740, 4549, 1395, 699, 2960, 2679, 3197, 8, 4057, 2709, 3115, 3436, 1190, 6629, 692, 3274, 5773, 8, 6997, 3536, 5936, 647, 3204, 1369, 1587
Offset: 2

Views

Author

V. Raman, Sep 27 2012

Keywords

Links

Crossrefs

Cf. A045875, A215727, A215728, A215729, A215730, A215731.

Programs

  • Mathematica
    Table[k = 1; While[! MemberQ[Partition[Differences[IntegerDigits[n^k]], 7, 1], {0, 0, 0, 0, 0, 0, 0}], k++]; k, {n, 2, 50}] (* T. D. Noe, Oct 01 2012 *)
lvk8[n_]:=Module[{k=Ceiling[Log[n,11111111]]},While[Max[Length/@ Split[ IntegerDigits[n^k]]]<8,k++];k] Array[lvk8, 50, 2] (* Harvey P. Dale, Jul 31 2013 *)

Extensions

Definition clarified by Harvey P. Dale, Jul 31 2013

A217164 a(n) is the least value of k such that the decimal expansion of n^k contains nine consecutive identical digits.

Original entry on oeis.org

42485, 22791, 21243, 2796, 27717, 33836, 14162, 22076, 9, 9443, 11429, 16661, 16548, 11259, 10622, 14991, 5786, 28096, 9, 2890, 16736, 14116, 4549, 1398, 27735, 7597, 3614, 10332, 9, 4057, 8497, 9060, 23985, 2943, 13859, 11422, 13270, 5773, 9, 14777, 11541
Offset: 2

Views

Author

V. Raman, Sep 27 2012

Keywords

Links

Crossrefs

Cf. A045875, A215727, A215728, A215729, A215730, A215731.

Programs

  • Mathematica
    Table[k = 1; While[! MemberQ[Partition[Differences[IntegerDigits[n^k]], 8, 1], {0, 0, 0, 0, 0, 0, 0, 0}], k++]; k, {n, 2, 50}] (* T. D. Noe, Oct 01 2012 *)
Showing 1-10 of 13 results. Next

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